Un Cig Ji教授講演会

講師: Un Cig Ji 氏 (韓国忠北国立大学教授)

題目: Evolution Systems and Continuity Equations forWhite Noise Functionals




 In this talk, we start with an application of the continuity equation

to the optimal transportation problem. By applying the quantum

decomposition of white noise functionals, the continuity equations

for white noise functionals are reformulated as time inhomogeneous

white noise differential equations.

We establish a systematic study of the evolution systems whose

infinitesimal generators are quadratic quantum white noises and

then as an application, we study the continuity equations for white

noise functionals of which the coefficient has up to the first chaos

(Gaussian process).

The restriction for the coefficient is comparable (not necessarily

equivalent) to the integrability condition of the exponential of the

coefficient by Ambrosio and Figalli for the well-posedness of the

continuity equation in the abstract Wiener space setting.